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Understanding an Earthquake of Magnitude 8.8

Two massive, tragic earthquakes punctuated the first months of 2010: first, a quake of 7.0 on the Moment Magnitude Scale ravaged Haiti, and six weeks later, a second quake of magnitude 8.8 shook central Chile. Both quakes were huge, both took many lives, and both toppled buildings and buckled roads. What's hard to comprehend, though, is that the Chilean quake was 500 times more powerful than the Haitian quake.

Humans are equipped to deal with small numbers--numbers we can count on our hands--but we're poorly designed to understand what it means when one quantity is 500 times greater than another.

The same problem afflicts us elsewhere. Hapless science teachers struggle to impress students with abstract numbers like 93 million (the number of miles separating the earth and the sun) and 1.3 million (the number of earths you could pack inside the sun). Bible sellers claim that 5 billion Bibles have been sold, and scholars of Mao Zedong suggest that the Little Red Book has sold 800 million copies.

These are staggering facts, but you'd be forgiven for finding them mind-numbing rather than mind-blowing. It's very difficult to imagine the difference between the numbers 1.3 million and 5 billion, even though 5 billion is nearly 4000 times larger than1.3 million. The question is how can communicators--teachers, scientists, and policymakers--do justice to figures of such impressive scope?

The solution is relatively simple: strive for concreteness. Big numbers are abstract entities, like the concepts of truth and morality, and they only make sense when we condense them to form bite-sized concrete nuggets.

Consider cosmic size and interstellar distance: one elegant model explains that if the sun were the size of a basketball, the earth would be the size of a pea. Everyone knows what peas and basketballs look like, and it's easy to imagine losing a pea in the palm of one hand while balancing a basketball precariously in the palm of the other. Using the same scale to represent distance, the pea-earth would be about 30 yards from the basketball-sun--roughly the length of a basketball court.

So, now, if you asked a child how accurate you'd need to be to launch a rocket to the sun, she might imagine holding a pea while standing at one end of a basketball court, peering at a basketball sitting at the opposite end of the court, and trying to propel a mote of dust (representing the rocket ship) from the pea to the basketball. And with that simple, concrete analogy, numbers like 93 million and 1.3 million start to make sense.

The same approach illuminates the difference between 5 billion Bibles and 800 million Little Red Books. These are the two best-selling books of all time, but the Little Red Book hardly competes with the Bible. Here's one way to understand that difference: imagine what it would be like to drive your car through a vast library filled with a single endless bookshelf. If you filled the bookshelf with every Little Red Book ever sold and drove as though you were on a high-speed interstate, you'd have to drive for five days without stopping before you'd exhaust the supply of books. Put another way, you could drive around the perimeter of the lower 48 United States alongside an unbroken train of Little Red Books. And what about the Bible? Suppose you wanted to find space for a single copy of your favorite book on the same endless bookshelf, this time filled with every Bible ever sold. Instead of driving for a measly five days, you'd have to drive for an entire month at interstate speeds before you'd pass the string of Bibles. Adopting a vertical analogy instead, if you dropped a basketball next to a stack of all the Bibles ever sold, the basketball would fall for an incredible three weeks before reaching the ground.

The simple but powerful fact is that we're capable of describing very large numbers with a bit of ingenuity and a basic understanding of how humans perceive quantity. Returning to the case of the two devastating earthquakes, just how much more powerful was the Chilean quake than the Haitian quake? Every human being on the planet would need to stop consuming energy for three hours to save as much energy as the magnitude 7.0 Haitian quake produced. The world would stop functioning as we know it for those three hours. We'd be without electricity, the internet, phones, and cars. Meanwhile, to match the output of the magnitude 8.8 Chilean quake, we'd need to renounce energy consumption for a whopping two months.

Sorry to poke an old article, but this is a topic that fascinates me--the way we chunk information so that even logarithmic growth seems like counting on our fingers.

I recently went to the trouble of expressing the "Wheat on a Chessboard" problem in concrete terms. That is, instead of just filling out a chessboard sized grid with the number that would come from doubling the quantities, I filled in the squares with quantities that where more easily digestible, so to speak. So, on my chessboard, I shift from counting grains of wheat to counting pounds of wheat at around the 14th square (based on a 50mg grain or wheat). At around the 25th square, I'm counting tonnes of wheat, and Mega-tonnes by the 46th. By around the 54th square, I've reached a year's worth of wheat production for the entire World (i.e. the amount of wheat the World eats in a year), and around 800 years of production by the end of the chessboard (as if the current production annual yield would have been constant for the past 800 years). Somehow that's a lot more meaningful then just 9223372036854775808.

Thanks for your post--that's a fantastic example, and one I hadn't come across before. It's a striking variant on the foolish king fable, where a wise girl convinces a foolish (and malevolent) king that she'll work for 20 days if he agrees to pay her 1c on the first day, 2c on the second day, 4c on the third, and so on, doubling the pay each day. Of course, the king calculates the amount in his head and stops somewhere around the 8th day, where she's earning little more than a dollar, and agrees to adopt that scheme. By the 20th day, the king has given over his kingdom and the girl becomes the new (benevolent) ruler. But I prefer your more vivid example!